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Showing 1 to 7 of 7 for “"Alexander polynomial"”.
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The Multivariable Alexander Polynomial on Tangles
The multivariable Alexander polynomial (MVA) is a classical invariant of knots and links. We give an extension to regular virtual knots which has simple versions of many of the relations known to hold for the classical invariant. By following the previous proofs that the MVA is of finite type we …
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On a Heegaard Floer theory for tangles
… The decategorification of HFL^ is the classical Alexander polynomial for links; likewise, the decategorification of HFT^ gives a local version ∇ˢ of the Alexander polynomial. In the first chapter of this thesis, we give a purely combinatorial definition of this polynomial invariant ∇ˢ via …
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Bordered Heegaard Floer Homology, Satellites, and Decategorification
… Floer homology categorifies the classical Alexander polynomial formula for satellites.
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The untwisting number of a knot
… changes needed to transform a knot into an Alexander polynomial-one knot. We work with a generalization of unknotting number due to Mathieu-Domergue, which we call the untwisting number. The p-untwisting number is the minimum number (over all diagrams of a knot) of full twists on at most 2p …
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New techniques in calculation of sutured instanton Floer homology: by Heegaard diagrams, Euler characteristics, and Dehn surgery formulae
… $K$ is a prime knot and the coefficients of the Alexander polynomial $\Delta_K(t)$ lie in $\{-1,0,1\}$. In particular, any hyperbolic alternating knot satisfies this property.
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Embedded contact knot homology and a surgery formula
… ECK in this situation which is equipped with an Alexander grading equivalent to that in the Heegaard Floer setting, categorifies the Alexander polynomial, and is conjecturally isomorphic to the hat version of knot Floer homology. The main result of this thesis is a large negative $n$-surgery …
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A ZETA FUNCTION FOR FLOWS WITH L(−1,−1) TEMPLATE
In this dissertation, we study the flows on R3 associated with a nonlinear system differential equation introduced by Clark Robinson in [46]. The periodic orbits are modeled by a semi-flow on the L(−1,−1) template. It is known that these are positive knots, but need not have positive braid …